


Using Incorporeality Effects for Other Side Reconnaissance

by Amaryllis Penndraig (bacontime)



Category: Worth the Candle
Genre: WorthTheCandle
Language: English
Status: Completed
Published: 2020-07-27
Updated: 2020-07-27
Packaged: 2021-03-06 02:55:37
Rating: General Audiences
Warnings: No Archive Warnings Apply
Chapters: 1
Words: 683
Publisher: archiveofourown.org
Story URL: https://archiveofourown.org/works/25526287
Author URL: https://archiveofourown.org/users/bacontime/pseuds/Amaryllis%20Penndraig
Comments: 1
Kudos: 6





	Using Incorporeality Effects for Other Side Reconnaissance

**1\. Internal Forces of a Thick Infinite Plan**

Suppose you have a flat disc with infinite radius, constant thickness _2H_ , and uniform density. Let height _h_ be the distance from the central plane of the disc, with positive and negative values of _h_ denoting the two different sides of the disc.

Let _−G_ be the gravitational acceleration experienced by a particle of mass _m_ on the positive surface of the disc, at _h = H_. It is a fact that the gravitational force on a particle near an infinite plane is independent of the particle’s distance to the plane. As such, if the particle is outside of the disc, then the gravitational force on the particle is simply _F = ±Gm_. And if the particle is inside the disc, then the gravitational force is proportional to the distance from the central plane.

The gravitational potential energy of the particle is found by integrating force over distance:

**2\. Traveling Through Aerb**

Now suppose an entad is used to render the particle intangible, so that only gravity exerts a force upon it, and the particle is free to fall through the mass of the disc. Acceleration is the second derivative of _h_ with respect to time, and combining this with the previous formula yields

This resembles the properties of a sinusoidal function. To verify, let _c(t)_ be the cosine of _t_ , _s(t)_ the sine of _t_ , and define _y = Ac(Bt)_. Then:

Substitute _h_ for _y_ to get

This equation holds if 

Thus the motion of the intangible particle can be described as a cosine with period and amplitude _H_. If the particle starts at _t = 0_ on the positive surface of the disc, then the position at time _t_ is given by the equation

The time needed to cross all the way through the disc and reach the negative surface is 

Applying these result to Aerb, the parameters are _G = 32 feet per second²_ , and _H = 4000mi = 21120000ft_.

Thus it would take an incorporeal particle ≈ 2552 seconds, or about 43 minutes, to pass through Aerb.

The Council of Arches has access to entads which can provide both the incorporeal effect and the supply of oxygen needed to last through the travel, and so disc-slipping should be considered as an option if it ever becomes strategically or economically important to travel to the Other Side.

**3\. Practical Complications**

Firstly, it is unknown how the currently available incorporeality entad interacts with heat and pressure. It may be necessary to take additional precautions to mitigate these effects.

Secondly, the surfaces of Aerb do not exhibit uniform altitude. If the exit point has higher altitude than the entry point, then the traveler will come to a stop underground, eventually reversing direction and returning to their entry point after passing through Aerb twice. If the exit point has lower altitude than the entry point, then the traveler will exit at extremely high speeds. Incorporeality protects the traveler in both of these situations, and attempts with large altitude differences can still be used to gain information about the terrain of the other side.

It is also likely that Aerb has increasing density towards the central plane, but this is not an issue by itself as such concentrations will only decrease travel time.

A more worrying issue is if the gravity equations above don’t model Aerbian forces at all. They are based on Earth data, which indicates that every particle pulls on every other particle with a force inversely proportional to the square of the distance between them. But suppose that the interior of Aerb exhibits inconsistent gravitational effects. For example, suppose that below 1600 feet, the acceleration entirely cuts off. Then the traveler will continue through Aerb at a velocity of 320 feet per second, and it will take over 36 hours for them to reach the other side.

Even worse, there could be unforeseeable anomalies deep underground. Hidden exclusion zones, regions that  
nullify entad magic, exotic radioactive ores, etc.

Taking all of these factors into consideration, it would be best to convince the renacim to carry out any experiments.


End file.
